Lagrangian transport evaluation of atmospheric chemistry in the Mediterranean region

Global observations of the chemical composition of the atmosphere are essential for understanding and studying the present and future state of the earth's atmosphere. However, by analyzing field experiments the consideration of the atmospheric motion is indispensable, because transport enables different chemical species, with different local natural and anthropogenic sources, to interact chemically and so consequently influences the chemical composition of the atmosphere. The distance over which that transport occurs is highly dependent upon meteorological conditions (e.g., wind speed, precipitation) and the properties of chemical species itself (e.g., solubility, reactivity). This interaction between chemistry and dynamics makes the study of atmospheric chemistry both difficult and challenging, and also demonstrates the relevance of including the atmospheric motions in that context. In this doctoral thesis the large-scale transport of air over the eastern Mediterranean region during summer 2001, with a focus on August during the Mediterranean Intensive Oxidant Study (MINOS) measurement campaign, was investigated from a lagrangian perspective. Analysis of back trajectories demonstrated transport of polluted air masses from western and eastern Europe in the boundary layer, from the North Atlantic/North American area in the middle end upper troposphere and additionally from South Asia in the upper troposphere towards the eastern Mediterranean. Investigation of air mass transport near the tropopause indicated enhanced cross-tropopause transport relative to the surrounding area over the eastern Mediterranean region in summer. A large band of air mass transport across the dynamical tropopause develops in June, and is shifted toward higher latitudes in July and August. This shifting is associated with the development and the intensification of the Arabian and South Asian upper-level anticyclones and consequential with areas of maximum clear-air turbulence, hypothesizing quasi-permanent areas with turbulent mixing of tropospheric and stratospheric air during summer over the eastern Mediterranean as a result of large-scale synoptic circulation. In context with the latex knowledge about the transport of polluted air masses towards the Mediterranean and with increasing emissions, especially in developing countries like India, this likely gains in importance.

Symplectic Lagrangian fibrations

In this work we investigate the deformation theory of pairs of an irreducible symplectic manifold X together with a Lagrangian subvariety Y in X, where the focus is on singular Lagrangian subvarieties. Among other things, Voisin's results [Voi92] are generalized to the case of simple normal crossing subvarieties; partial results are also obtained for more complicated singularities.rnAs done in Voisin's article, we link the codimension of the subspace of the universal deformation space of X parametrizing those deformations where Y persists, to the rank of a certain map in cohomology. This enables us in some concrete cases to actually calculate or at least estimate the codimension of this particular subspace. In these cases the Lagrangian subvarieties in question occur as fibers or fiber components of a given Lagrangian fibration f : X --> B. We discuss examples and the question of how our results might help to understand some aspects of Lagrangian fibrations.

The geometry of Lagrangian fibres

If the generic fibre f−1(c) of a Lagrangian fibration f : X → B on a complex Poisson– variety X is smooth, compact, and connected, it is isomorphic to the compactification of a complex abelian Lie–group. For affine Lagrangian fibres it is not clear what the structure of the fibre is. Adler and van Moerbeke developed a strategy to prove that the generic fibre of a Lagrangian fibration is isomorphic to the affine part of an abelian variety.rnWe extend their strategy to verify that the generic fibre of a given Lagrangian fibration is the affine part of a (C∗)r–extension of an abelian variety. This strategy turned out to be successful for all examples we studied. Additionally we studied examples of Lagrangian fibrations that have the affine part of a ramified cyclic cover of an abelian variety as generic fibre. We obtained an embedding in a Lagrangian fibration that has the affine part of a C∗–extension of an abelian variety as generic fibre. This embedding is not an embedding in the category of Lagrangian fibrations. The C∗–quotient of the new Lagrangian fibration defines in a natural way a deformation of the cyclic quotient of the original Lagrangian fibration.

Mesonic chiral perturbation theory - odd intrinsic parity sector

In der vorliegenden Dissertation werden zwei verschiedene Aspekte des Sektors ungerader innerer Parität der mesonischen chiralen Störungstheorie (mesonische ChPT) untersucht. Als erstes wird die Ein-Schleifen-Renormierung des führenden Terms, der sog. Wess-Zumino-Witten-Wirkung, durchgeführt. Dazu muß zunächst der gesamte Ein-Schleifen-Anteil der Theorie mittels Sattelpunkt-Methode extrahiert werden. Im Anschluß isoliert man alle singulären Ein-Schleifen-Strukturen im Rahmen der Heat-Kernel-Technik. Zu guter Letzt müssen diese divergenten Anteile absorbiert werden. Dazu benötigt man eine allgemeinste anomale Lagrange-Dichte der Ordnung O(p^6), welche systematisch entwickelt wird. Erweitert man die chirale Gruppe SU(n)_L x SU(n)_R auf SU(n)_L x SU(n)_R x U(1)_V, so kommen zusätzliche Monome ins Spiel. Die renormierten Koeffizienten dieser Lagrange-Dichte, die Niederenergiekonstanten (LECs), sind zunächst freie Parameter der Theorie, die individuell fixiert werden müssen. Unter Betrachtung eines komplementären vektormesonischen Modells können die Amplituden geeigneter Prozesse bestimmt und durch Vergleich mit den Ergebnissen der mesonischen ChPT eine numerische Abschätzung einiger LECs vorgenommen werden. Im zweiten Teil wird eine konsistente Ein-Schleifen-Rechnung für den anomalen Prozeß (virtuelles) Photon + geladenes Kaon -> geladenes Kaon + neutrales Pion durchgeführt. Zur Kontrolle unserer Resultate wird eine bereits vorhandene Rechnung zur Reaktion (virtuelles) Photon + geladenes Pion -> geladenes Pion + neutrales Pion reproduziert. Unter Einbeziehung der abgeschätzten Werte der jeweiligen LECs können die zugehörigen hadronischen Strukturfunktionen numerisch bestimmt und diskutiert werden.

Lagrange-Singularitäten

In dieser Arbeit wird eine Deformationstheorie fürLagrange-Singularitäten entwickelt. Wir definieren einen Komplex von Moduln mit nicht-linearem Differential, densogenannten Lagrange-de Rham-Komplex, dessen ersteKohomologie isomorph zum Raum der infinitesimalenLagrange-Deformationen ist. Wir beschreiben die Beziehung diesesKomplexes zur Theorie der Moduln über dem Ring vonDifferentieloperatoren. Informationen zur Obstruktionstheorie vonLagrange-Deformationen werden aus derzweiten Kohomologie des Lagrange-de Rham-Komplexes gewonnen.Wir zeigen, dass unter einer geometrischen Bedingung an dieSingularität ie Kohomologie von des Lagrange-deRham-Komplexes ausendlich dimensionalen Vektorräumen besteht. Desweiteren wirdeine Methode zur effektiven Berechnung dieser Kohomologie fürquasi-homogene Lagrange-Flächensingularitäten entwickelt. UnterZuhilfenahme von Computeralgebra wird diese Methode für konkreteBeispiele angewendet.

Novel simulation methods for Coulomb and hydrodynamic interactions

This thesis presents new methods to simulate systems with hydrodynamic and electrostatic interactions. Part 1 is devoted to computer simulations of Brownian particles with hydrodynamic interactions. The main influence of the solvent on the dynamics of Brownian particles is that it mediates hydrodynamic interactions. In the method, this is simulated by numerical solution of the Navier--Stokes equation on a lattice. To this end, the Lattice--Boltzmann method is used, namely its D3Q19 version. This model is capable to simulate compressible flow. It gives us the advantage to treat dense systems, in particular away from thermal equilibrium. The Lattice--Boltzmann equation is coupled to the particles via a friction force. In addition to this force, acting on {it point} particles, we construct another coupling force, which comes from the pressure tensor. The coupling is purely local, i.~e. the algorithm scales linearly with the total number of particles. In order to be able to map the physical properties of the Lattice--Boltzmann fluid onto a Molecular Dynamics (MD) fluid, the case of an almost incompressible flow is considered. The Fluctuation--Dissipation theorem for the hybrid coupling is analyzed, and a geometric interpretation of the friction coefficient in terms of a Stokes radius is given. Part 2 is devoted to the simulation of charged particles. We present a novel method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. This algorithm scales linearly, too. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. The Lagrangian formulation of the coupled particles--fields system is derived. The quasi--Hamiltonian dynamics of the system is studied in great detail. For implementation on the computer, the equations of motion are discretized with respect to both space and time. The discretization of the electromagnetic fields on a lattice, as well as the interpolation of the particle charges on the lattice is given. The algorithm is as local as possible: Only nearest neighbors sites of the lattice are interacting with a charged particle. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method allows easy parallelization using standard domain decomposition. Some benchmarking results of the algorithm are presented and discussed.

Modeling surface-atmosphere exchange of trace gases and energy within and above the Amazon rain forest

Die vorliegende Dissertation untersucht die biogeochemischen Vorgänge in der Vegetationsschicht (Bestand) und die Rückkopplungen zwischen physiologischen und physikalischen Umweltprozessen, die das Klima und die Chemie der unteren Atmosphäre beeinflussen. Ein besondere Schwerpunkt ist die Verwendung theoretischer Ansätze zur Quantifizierung des vertikalen Austauschs von Energie und Spurengasen (Vertikalfluss) unter besonderer Berücksichtigung der Wechselwirkungen der beteiligten Prozesse. Es wird ein differenziertes Mehrschicht-Modell der Vegetation hergeleitet, implementiert, für den amazonischen Regenwald parametrisiert und auf einen Standort in Rondonia (Südwest Amazonien) angewendet, welches die gekoppelten Gleichungen zur Energiebilanz der Oberfläche und CO2-Assimilation auf der Blattskala mit einer Lagrange-Beschreibung des Vertikaltransports auf der Bestandesskala kombiniert. Die hergeleiteten Parametrisierungen beinhalten die vertikale Dichteverteilung der Blattfläche, ein normalisiertes Profil der horizontalen Windgeschwindigkeit, die Lichtakklimatisierung der Photosynthesekapazität und den Austausch von CO2 und Wärme an der Bodenoberfläche. Desweiteren werden die Berechnungen zur Photosynthese, stomatären Leitfähigkeit und der Strahlungsabschwächung im Bestand mithilfe von Feldmessungen evaluiert. Das Teilmodell zum Vertikaltransport wird im Detail unter Verwendung von 222-Radon-Messungen evaluiert. Die ``Vorwärtslösung'' und der ``inverse Ansatz'' des Lagrangeschen Dispersionsmodells werden durch den Vergleich von beobachteten und vorhergesagten Konzentrationsprofilen bzw. Bodenflüssen bewertet. Ein neuer Ansatz wird hergeleitet, um die Unsicherheiten des inversen Ansatzes aus denjenigen des Eingabekonzentrationsprofils zu quantifizieren. Für nächtliche Bedingungen wird eine modifizierte Parametrisierung der Turbulenz vorgeschlagen, welche die freie Konvektion während der Nacht im unteren Bestand berücksichtigt und im Vergleich zu früheren Abschätzungen zu deutlich kürzeren Aufenthaltszeiten im Bestand führt. Die vorhergesagte Stratifizierung des Bestandes am Tage und in der Nacht steht im Einklang mit Beobachtungen in dichter Vegetation. Die Tagesgänge der vorhergesagten Flüsse und skalaren Profile von Temperatur, H2O, CO2, Isopren und O3 während der späten Regen- und Trockenzeit am Rondonia-Standort stimmen gut mit Beobachtungen überein. Die Ergebnisse weisen auf saisonale physiologische Änderungen hin, die sich durch höhere stomatäre Leitfähigkeiten bzw. niedrigere Photosyntheseraten während der Regen- und Trockenzeit manifestieren. Die beobachteten Depositionsgeschwindigkeiten für Ozon während der Regenzeit überschreiten diejenigen der Trockenzeit um 150-250%. Dies kann nicht durch realistische physiologische Änderungen erklärt werden, jedoch durch einen zusätzlichen cuticulären Aufnahmemechanismus, möglicherweise an feuchten Oberflächen. Der Vergleich von beobachteten und vorhergesagten Isoprenkonzentrationen im Bestand weist auf eine reduzierte Isoprenemissionskapazität schattenadaptierter Blätter und zusätzlich auf eine Isoprenaufnahme des Bodens hin, wodurch sich die globale Schätzung für den tropischen Regenwald um 30% reduzieren würde. In einer detaillierten Sensitivitätsstudie wird die VOC Emission von amazonischen Baumarten unter Verwendung eines neuronalen Ansatzes in Beziehung zu physiologischen und abiotischen Faktoren gesetzt. Die Güte einzelner Parameterkombinationen bezüglich der Vorhersage der VOC Emission wird mit den Vorhersagen eines Modells verglichen, das quasi als Standardemissionsalgorithmus für Isopren dient und Licht sowie Temperatur als Eingabeparameter verwendet. Der Standardalgorithmus und das neuronale Netz unter Verwendung von Licht und Temperatur als Eingabeparameter schneiden sehr gut bei einzelnen Datensätzen ab, scheitern jedoch bei der Vorhersage beobachteter VOC Emissionen, wenn Datensätze von verschiedenen Perioden (Regen/Trockenzeit), Blattentwicklungsstadien, oder gar unterschiedlichen Spezies zusammengeführt werden. Wenn dem Netzwerk Informationen über die Temperatur-Historie hinzugefügt werden, reduziert sich die nicht erklärte Varianz teilweise. Eine noch bessere Leistung wird jedoch mit physiologischen Parameterkombinationen erzielt. Dies verdeutlicht die starke Kopplung zwischen VOC Emission und Blattphysiologie.

Regularisierung und Renormierung in der Quantenfeldtheorie : Resultate aus dem Vergleich konsistenter und praktikabler Methoden

Die Arbeit beginnt mit dem Vergleich spezieller Regularisierungsmethoden in der Quantenfeldtheorie mit dem Verfahren zur störungstheoretischen Konstruktion der S-Matrix nach Epstein und Glaser. Da das Epstein-Glaser-Verfahren selbst als Regularisierungsverfahren verwandt werden kann und darüberhinaus ausschließlich auf physikalisch motivierten Postulaten basiert, liefert dieser Vergleich ein Kriterium für die Zulässigkeit anderer Regularisierungsmethoden. Zusätzlich zur Herausstellung dieser Zulässigkeit resultiert aus dieser Gegenüberstellung als weiteres wesentliches Resultat ein neues, in der Anwendung praktikables sowie konsistentes Regularisierungsverfahren, das modifizierte BPHZ-Verfahren. Dieses wird anhand von Ein-Schleifen-Diagrammen aus der QED (Elektronselbstenergie, Vakuumpolarisation und Vertexkorrektur) demonstriert. Im Gegensatz zur vielverwandten Dimensionalen Regularisierung ist dieses Verfahren uneingeschränkt auch für chirale Theorien anwendbar. Als Beispiel hierfür dient die Berechnung der im Rahmen einer axialen Erweiterung der QED-Lagrangedichte auftretenden U(1)-Anomalie. Auf der Stufe von Mehr-Schleifen-Diagrammen zeigt der Vergleich der Epstein-Glaser-Konstruktion mit dem bekannten BPHZ-Verfahren an mehreren Beispielen aus der Phi^4-Theorie, darunter das sog. Sunrise-Diagramm, daß zu deren Berechnung die nach der Waldformel des BPHZ-Verfahrens zur Regularisierung beitragenden Unterdiagramme auf eine kleinere Klasse eingeschränkt werden können. Dieses Resultat ist gleichfalls für die Praxis der Regularisierung bedeutsam, da es bereits auf der Stufe der zu berücksichtigenden Unterdiagramme zu einer Vereinfachung führt.

Black-scholes type equations

In this work we are concerned with the analysis and numerical solution of Black-Scholes type equations arising in the modeling of incomplete financial markets and an inverse problem of determining the local volatility function in a generalized Black-Scholes model from observed option prices. In the first chapter a fully nonlinear Black-Scholes equation which models transaction costs arising in option pricing is discretized by a new high order compact scheme. The compact scheme is proved to be unconditionally stable and non-oscillatory and is very efficient compared to classical schemes. Moreover, it is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. In the next chapter we turn to the calibration problem of computing local volatility functions from market data in a generalized Black-Scholes setting. We follow an optimal control approach in a Lagrangian framework. We show the existence of a global solution and study first- and second-order optimality conditions. Furthermore, we propose an algorithm that is based on a globalized sequential quadratic programming method and a primal-dual active set strategy, and present numerical results. In the last chapter we consider a quasilinear parabolic equation with quadratic gradient terms, which arises in the modeling of an optimal portfolio in incomplete markets. The existence of weak solutions is shown by considering a sequence of approximate solutions. The main difficulty of the proof is to infer the strong convergence of the sequence. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution, but without additional regularity assumptions on the solution. The results are illustrated by a numerical example.

Renormalization of fermion mixing

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by hermiticity. After analysing the complete renormalized Lagrangian in a general theory including vector and scalar bosons with arbitrary renormalizable interactions, we consider two specific models: quark mixing in the electroweak Standard Model and mixing of Majorana neutrinos in the seesaw mechanism. A counter term for fermion mixing matrices can not be fixed by only taking into account self-energy corrections or fermion field renormalization constants. The presence of unstable particles in the theory can lead to a non-unitary renormalized mixing matrix or to a gauge parameter dependence in its counter term. Therefore, we propose to determine the mixing matrix counter term by fixing the complete correction terms for a physical process to experimental measurements. As an example, we calculate the decay rate of a top quark and of a heavy neutrino. We provide in each of the chosen models sample calculations that can be easily extended to other theories.

The Euler number of OGradys 10-dimensional symplectic manifold

Wir berechnen die Eulerzahl der 10-dimensionalen exzeptionellen irreduziblen symplektischen Mannigfaltigkeit, die von O Grady konstruiert wurde. Die Idee besteht darin, zunächst eine Lagrangefaserung zu konstruieren und dann die Eulerzahlen der Fasern zu berechnen. Es stellt sich heraus, dass fast alle Fasern die Eulerzahl 0 haben, und deswegen reduziert sich das Problem auf die Berechnung der Eulerzahlen der übrigen Fasern. Diese Fasern sind Modulräume von halbstabilen Garben auf singulären Kurven. Der Hauptteil dieser Dissertation ist der Berechnung der Eulerzahlen dieser Modulräume gewidmet. Diese Resultate sind von unabhängigem Interesse.

Chirale Störungsrechnung im Sektor ungerader innerer Parität bis zur chiralen Ordnung O(q 6)

Die vorliegende Dissertation behandelt den anomalen Sektor bzw. den Sektor ungerader innerer Parität in mesonischer chiraler Störungsrechnung (mesonische ChPT) bis zur chiralen Ordnung O(q^6). Auf eine Einführung in die Quantenchromodynamik (QCD) und ihrer Verknüpfung mit der chiralen Symmetrie folgt die Betrachtung der mesonischen ChPT im Sektor gerader sowie ungerader innerer Parität bis zur Ordnung O(q^4). Der sogenannte Wess-Zumino-Witten Term, welcher den Einfluss der axialen Anomalie bezogen auf die ChPT widerspiegelt, wird studiert. Anschließend wird die allgemeinste Lagrangedichte der Ordnung O(q^6) im Sektor ungerader innerer Parität detailiert analysiert. Sie enthält in ihrer SU(3)-Formulierung 23 Niederenergiekonstanten(low-energy constant=LEC). Aus Sicht der ChPT sind diese LECs freie Parameter, die auf irgendeine Art und Weise fixiert werden müssen. Es wird herausgearbeitet, bei welchen Prozessen und in welchen Kombinationen die jeweiligen LECs auftreten. Daraufhin wird versucht so viele dieser LECs wie möglich mittels Vektormesondominanz (VMD) sowie experimenteller Daten abzuschätzen und anzupassen. Hierfür wird zuerst die Vorgehensweise einer konsistenten Rechnung im Sektor ungerader innerer Parität bis zur Ordnung O(q^6) studiert, gefolgt von der Berechnung von insgesamt vierzehn geeigneten Prozessen im Rahmen der ChPT bis zur Ordnung O(q^6). Unter Verwendung experimenteller Daten werden dreizehn der LECs angepasst, wobei gegenwärtig nicht bei allen betrachteten Prozessen experimentelle Daten zur Verfügung stehen. Die Ergebnisse werden diskutiert und Unterschiede bzw. Übereinstimmungen mit anderen Rechnungen herausgearbeitet. Zusammenfassend erhält man einen umfassenden Einblick in den Sektor ungerader innerer Parität in mesonischer ChPT bis zur Ordnung O(q^6).

Exploring physical processes related to past climate proxies: lake sediments and stable water isotopes

Proxy data are essential for the investigation of climate variability on time scales larger than the historical meteorological observation period. The potential value of a proxy depends on our ability to understand and quantify the physical processes that relate the corresponding climate parameter and the signal in the proxy archive. These processes can be explored under present-day conditions. In this thesis, both statistical and physical models are applied for their analysis, focusing on two specific types of proxies, lake sediment data and stable water isotopes.rnIn the first part of this work, the basis is established for statistically calibrating new proxies from lake sediments in western Germany. A comprehensive meteorological and hydrological data set is compiled and statistically analyzed. In this way, meteorological times series are identified that can be applied for the calibration of various climate proxies. A particular focus is laid on the investigation of extreme weather events, which have rarely been the objective of paleoclimate reconstructions so far. Subsequently, a concrete example of a proxy calibration is presented. Maxima in the quartz grain concentration from a lake sediment core are compared to recent windstorms. The latter are identified from the meteorological data with the help of a newly developed windstorm index, combining local measurements and reanalysis data. The statistical significance of the correlation between extreme windstorms and signals in the sediment is verified with the help of a Monte Carlo method. This correlation is fundamental for employing lake sediment data as a new proxy to reconstruct windstorm records of the geological past.rnThe second part of this thesis deals with the analysis and simulation of stable water isotopes in atmospheric vapor on daily time scales. In this way, a better understanding of the physical processes determining these isotope ratios can be obtained, which is an important prerequisite for the interpretation of isotope data from ice cores and the reconstruction of past temperature. In particular, the focus here is on the deuterium excess and its relation to the environmental conditions during evaporation of water from the ocean. As a basis for the diagnostic analysis and for evaluating the simulations, isotope measurements from Rehovot (Israel) are used, provided by the Weizmann Institute of Science. First, a Lagrangian moisture source diagnostic is employed in order to establish quantitative linkages between the measurements and the evaporation conditions of the vapor (and thus to calibrate the isotope signal). A strong negative correlation between relative humidity in the source regions and measured deuterium excess is found. On the contrary, sea surface temperature in the evaporation regions does not correlate well with deuterium excess. Although requiring confirmation by isotope data from different regions and longer time scales, this weak correlation might be of major importance for the reconstruction of moisture source temperatures from ice core data. Second, the Lagrangian source diagnostic is combined with a Craig-Gordon fractionation parameterization for the identified evaporation events in order to simulate the isotope ratios at Rehovot. In this way, the Craig-Gordon model can be directly evaluated with atmospheric isotope data, and better constraints for uncertain model parameters can be obtained. A comparison of the simulated deuterium excess with the measurements reveals that a much better agreement can be achieved using a wind speed independent formulation of the non-equilibrium fractionation factor instead of the classical parameterization introduced by Merlivat and Jouzel, which is widely applied in isotope GCMs. Finally, the first steps of the implementation of water isotope physics in the limited-area COSMO model are described, and an approach is outlined that allows to compare simulated isotope ratios to measurements in an event-based manner by using a water tagging technique. The good agreement between model results from several case studies and measurements at Rehovot demonstrates the applicability of the approach. Because the model can be run with high, potentially cloud-resolving spatial resolution, and because it contains sophisticated parameterizations of many atmospheric processes, a complete implementation of isotope physics will allow detailed, process-oriented studies of the complex variability of stable isotopes in atmospheric waters in future research.rn

Feasibility studies of the pp pi 0 e + e - electromagnetic channel at PANDA

Among all possible realizations of quark and antiquark assembly, the nucleon (the proton and the neutron) is the most stable of all hadrons and consequently has been the subject of intensive studies. Mass, shape, radius and more complex representations of its internal structure are measured since several decades using different probes. The proton (spin 1/2) is described by the electric GE and magnetic GM form factors which characterise its internal structure. The simplest way to measure the proton form factors consists in measuring the angular distribution of the electron-proton elastic scattering accessing the so-called Space-Like region where q2 < 0. Using the crossed channel antiproton proton <--> e+e-, one accesses another kinematical region, the so-called Time-Like region where q2 > 0. However, due to the antiproton proton <--> e+e- threshold q2th, only the kinematical domain q2 > q2th > 0 is available. To access the unphysical region, one may use the antiproton proton --> pi0 e+ e- reaction where the pi0 takes away a part of the system energy allowing q2 to be varied between q2th and almost 0. This thesis aims to show the feasibility of such measurements with the PANDA detector which will be installed on the new high intensity antiproton ring at the FAIR facility at Darmstadt. To describe the antiproton proton --> pi0 e+ e- reaction, a Lagrangian based approach is developed. The 5-fold differential cross section is determined and related to linear combinations of hadronic tensors. Under the assumption of one nucleon exchange, the hadronic tensors are expressed in terms of the 2 complex proton electromagnetic form factors. An extraction method which provides an access to the proton electromagnetic form factor ratio R = |GE|/|GM| and for the first time in an unpolarized experiment to the cosine of the phase difference is developed. Such measurements have never been performed in the unphysical region up to now. Extended simulations were performed to show how the ratio R and the cosine can be extracted from the positron angular distribution. Furthermore, a model is developed for the antiproton proton --> pi0 pi+ pi- background reaction considered as the most dangerous one. The background to signal cross section ratio was estimated under different cut combinations of the particle identification information from the different detectors and of the kinematic fits. The background contribution can be reduced to the percent level or even less. The corresponding signal efficiency ranges from a few % to 30%. The precision on the determination of the ratio R and of the cosine is determined using the expected counting rates via Monte Carlo method. A part of this thesis is also dedicated to more technical work with the study of the prototype of the electromagnetic calorimeter and the determination of its resolution.

Higher-order perturbative relativistic corrections to energies and properties

Relativistic effects need to be considered in quantum-chemical calculations on systems including heavy elements or when aiming at high accuracy for molecules containing only lighter elements. In the latter case, consideration of relativistic effects via perturbation theory is an attractive option. Among the available techniques, Direct Perturbation Theory (DPT) in its lowest order (DPT2) has become a standard tool for the calculation of relativistic corrections to energies and properties.In this work, the DPT treatment is extended to the next order (DPT4). It is demonstrated that the DPT4 correction can be obtained as a second derivative of the energy with respect to the relativistic perturbation parameter. Accordingly, differentiation of a suitable Lagrangian, thereby taking into account all constraints on the wave function, provides analytic expressions for the fourth-order energy corrections. The latter have been implemented at the Hartree-Fock level and within second-order Møller-Plesset perturbaton theory using standard analytic second-derivative techniques into the CFOUR program package. For closed-shell systems, the DPT4 corrections consist of higher-order scalar-relativistic effects as well as spin-orbit corrections with the latter appearing here for the first time in the DPT series.Relativistic corrections are reported for energies as well as for first-order electrical properties and compared to results from rigorous four-component benchmark calculations in order to judge the accuracy and convergence of the DPT expansion for both the scalar-relativistic as well as the spin-orbit contributions. Additionally, the importance of relativistic effects to the bromine and iodine quadrupole-coupling tensors is investigated in a joint experimental and theoretical study concerning the rotational spectra of CH2BrF, CHBrF2, and CH2FI.